Mempool Leakage Thresholds and Sandwich Attack Profitability

Summary

The paper studies how much information a private mempool can leak before a sandwich attack becomes profitable. Its model uses a fee-free constant-product automated market maker and assumes attackers know the token pair and trade direction, while seeing only an interval for the victim’s trade size. The attacker bids in a first-price auction for the opportunity and must keep the victim’s trade executable across the entire interval.

The analysis finds that the interval’s lower bound determines which front-runs are feasible, and that the largest feasible front-run maximizes several stated profit criteria. It derives a threshold for when hiding size information can rule out sandwiches that profit across all consistent sizes. The results also cover auction rent with multiple symmetric traders, hidden trade direction, and post-trade arbitrage. These conclusions depend on the specified AMM and auction assumptions; they are not a general guarantee for other market designs or execution costs.

Key ideas

• The analysis models sandwich attacks against a fee-free constant-product automated market maker.
• When trade size is leaked as an interval, its smallest consistent value determines feasible front-runs.
• The largest feasible front-run is optimal under the paper’s pointwise, expected, and worst-case profit criteria.
• The paper derives a size-leakage threshold for preventing sandwiches profitable at every consistent size.
• Hidden direction can prevent a single unconditional first leg, while post-trade arbitrage may remain possible.

Tags

# How Much Must a Private Mempool Hide? Exact Leakage Thresholds for Sandwich Attacks


# How Much Must a Private Mempool Hide? Exact Leakage Thresholds for Sandwich Attacks









Private and encrypted mempools hide pending transactions to stop sandwich attacks and other forms of maximal extractable value (MEV), but what they hide is rarely everything: a transaction's pair, direction, and a coarse range for its size can still leak. How much leakage makes sandwiching pay? We answer exactly for a fee-free constant-product automated market maker, the pricing rule behind Uniswap v2. Traders observe an interval containing the victim's size and bid in a first-price auction for the right to sandwich it, and the winning front-run must keep the victim's trade executable at every size in the interval. The answer turns on the smallest size consistent with the leak. It alone determines the feasible front-runs, the largest feasible front-run is optimal for pointwise, expected, and worst-case profit alike, and the guaranteed profit has a closed form. When execution is costly, a privacy layer that wants to rule out sandwiches profitable at every consistent size may therefore reveal anything about the size except a lower bound above an explicit threshold; the upper end of the range is irrelevant. With two or more symmetric traders, every pure-strategy perfect Bayesian equilibrium of the auction hands the entire expected net rent to the auctioneer. If the direction is hidden too, no non-contingent first leg front-runs both possible directions, while post-trade arbitrage can survive even perfect pre-trade hiding.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.